I think the word "democracy" is doing a lot of heavy lifting in the OP. Democracy implies that power is somewhat widespread among the population – while universal suffrage has been fairly uncommon, things like "all landowners get the vote" and the like are generally recognized as (imperfect) democracies, and I don't think that's what they're going for. That's a bit too diffuse for political elements in a game, where PCs who want to influence politics would need to employ tools like propaganda rather than heroic deeds and/or favors.
What they're actually going for seems more like "factions": a manageable number of groups, often with a representative head, wielding formal or informal power mostly in their own right without being beholden to a central figure for that power. These factions generally come in two types, which we can call professional and political.
A professional faction is one that controls a particular pillar of society. This could be "the Church", "the Craftsmen", "the Army", "the Navy", "the Law", and so on. A political faction is one that's united by a common desire to control the state and move it in a particular direction. Sometimes this can be an idealistic goal ("We believe this to be the best way forward."), like many political parties claim to have, while others it's more of a tribal thing ("We want the house of Bourbon to be on top.").
Often, you have both types of factions, with political factions having various levels of influence among the professional factions. A good example to look at here for a large-scale state is the Realm in Exalted. The Realm is currently governed by 11 Great Houses that each have various levels of influence in assorted power centers: the Legions, the Immaculate Order, the various directional Navies, and so on. 11 houses is probably too much for an RPG (it gets hard to keep track of them unless they're the central focus of a campaign and everyone has a high level of buy-in), but it serves as an example of how the two levels of factions intersect.